Solving linear equations – a guide for Grades 6–8
An equation is like a balanced scale: both sides must stay equal. Whatever you do to one side, you must also do to the other.
1. Isolate x with addition or subtraction
Grade 6Remove the number beside x by using the inverse operation.
Steps
- 1Subtract 7 from both sides.
- 2Only x remains on the left.
- 3Check that 12 + 7 = 19.
x + 7 = 19 | −7 x = 12
⚠️ Common mistake: The −7 must be applied to both sides.
✏️ Try it yourself: x − 9 = 16
Show answer
Answer: x = 25
2. Remove the coefficient of x
Grade 64x means 4 · x, so divide both sides by 4.
Steps
- 1Divide the left and right sides by 4.
- 24x ÷ 4 becomes x.
- 3Check that 4 · 7 = 28.
4x = 28 | ÷4 x = 7
⚠️ Common mistake: Do not divide only the number on the right.
✏️ Try it yourself: 6x = 54
Show answer
Answer: x = 9
3. Two-step equations
Grades 6–7Undo addition or subtraction first, then multiplication or division.
Steps
- 1Subtract 5 from both sides.
- 2This gives 3x = 21.
- 3Divide both sides by 3.
3x + 5 = 26 3x = 21 x = 7
⚠️ Common mistake: Order matters: remove +5 before dividing by 3.
✏️ Try it yourself: 4x − 6 = 22
Show answer
Answer: x = 7
4. x on both sides
Grade 7Collect all x terms on one side and all numbers on the other.
Steps
- 1Subtract 2x from both sides.
- 2Then add 4 to both sides.
- 3Divide 12 by 3.
5x − 4 = 2x + 8 3x = 12 x = 4
⚠️ Common mistake: Terms do not magically change signs—apply the same operation to both sides.
✏️ Try it yourself: 7x + 3 = 4x + 18
Show answer
Answer: x = 5
5. Expand brackets
Grades 7–8Multiply the number outside the brackets by every term inside.
Steps
- 1Multiply both x and 4 by 3.
- 2This gives 3x + 12 = 30.
- 3Continue as a two-step equation.
3(x + 4) = 30 3x + 12 = 30 x = 6
⚠️ Common mistake: The 3 must also multiply the 4.
✏️ Try it yourself: 4(x − 2) = 24
Show answer
Answer: x = 8
6. Check the solution
Grades 6–8Substitute your value of x into the original equation.
Steps
- 1Substitute x = 4.
- 2Calculate both sides separately.
- 3If both sides match, the solution is correct.
5 · 4 − 4 = 2 · 4 + 8 16 = 16 ✓
⚠️ Common mistake: Always check using the original equation.
✏️ Try it yourself: Check x = 5 in 3x + 2 = 17.
Show answer
Answer: 15 + 2 = 17 ✓
Practise equations
Create new equations for Grade 6, 7 or 8.